AM 20 Homework 2
matlab | lab – 这道题目是利用matlab进行的编程代写任务, 涵盖了matlab等程序代做方面, 这是值得参考的lab代写的题目
Problem 1.Find the general solution of the following ODEs.
= 2 y+t+et (1) dy dt = 2 ty+et 2 (2) dy dt = y+ sin 3t (3)
Problem 2.Solve the following initial value problems
dy dt 4 y=et, y(t= 0) = 1 (4)
t dy dt + 2y=t^2 t+ 1, y(t= 1) = 0. 5 , t > 0 (5)
Problem 3.Consider the following differential equation.
dy dt = 2y1 + 5 sin(t).
- Find the general solution to this equation.
- Find the value ofy 0 such that the solution starting from initial conditiony(0) =y 0 remains finite ast
Problem 4.Solve the following initial value problem and identify the interval of definition.
t y= 4t3 +
t , y(1) = 2
Problem 5. Without solving the equations, determine the longest interval in which the given initial value problem is certain to have a unique solution.
lnt t 5 y = 2t, y(1) = 2
Problem 6. Show that ifaandare positive constants, andbis any real number, then every solution of the equation
+ay = bet
has the property that limty(t) = 0. (Hint: consider the casesa=anda 6 =separately.)
Problem 7. Find the solutions (in explicit form) of the following initial value problems; and determine the interval in which the solutions are defined. dy dt
1 2 t y , y(t= 1) = 2 (6)
t+yet dy dt = 0, y(t= 0) = 1 (7) dy dt
2 t y+t^2 y , y(t= 0) = 2 (8) dy dt
3 t^2 et 2 y 5 , y(t= 0) = 1 (9)
Problem 8.Given an initial value value problem of the following differential equation
dy dt = ay+u(t), y(0) =y 0 (10)
y(t) =y 0 eat+eat
is the solution to this initial value problem.